Page - Stevenson, Chapter 5, Strategic Capacity Planning
Evaluating Capacity Alternatives (Problems 1 & 3, in class; problems 4 & 5 HW)
Fixed Costs (FC): Rent, insurance, utilities,
Variable Costs (VC): costs to produce
Total Costs (TC) = FC + (VC * Quantity)
Total Revenue (TR) = Revenue * Q
Profit (P) = TR - TC
P= (R * Q) – ((FC +(VC * Q))
P= Q (R – VC) – FC
Quantity for Breakeven Point (QBEP)
QBEP is where TR=TC
QBEP =
FC
R - VC
In a capacity decision, would you want to purchase a machine with
a capacity less than QBEP? Why or why not?
Quantity Needed for a specified level of profitability
Q = P + FC
R - VC
How does this relate to capacity decisions?
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Example
Page 192, Number 3
FC = $9,200/month
VC = $.70/unit
Price (Revenue) = $.90/unit
a. determine the volume/month required to breakeven
QBEP =
FC
R – VC
= $ 9,200
.90 -.70
= $9,200
.20
= 46,000 pieces of pottery per month
What if the property being considered has a maximum capacity of
40,000 pieces of pottery/month. What is your recommendation?
b. What profit would be realized on a monthly volume of 61,000
pieces? Of 87,000 pieces?
P = Q ( R – VC) – FC
P = 61, 000 (.90-.70) – 9,200
P = 61,000(.20) – 9,200
P = 12,200 – 9,200
P= $3,000
Profit for a volume of 87,000 pieces of pottery
P = Q ( R – VC) – FC
P = 87,000 (.90-.70) – 9,200
2
P = 87,000 (.20) – 9,200
P = $17,400 - $9,200
P = $8,200
C. what volume is needed to obtain a profit of $16,000/month
Q = P + FC
R - VC
Q = 16, 000 + 9,200
.90 - .70
Q = 25,200
.20
Q= 126, 000 Units
D. what volume is needed to provide revenue of $23,000 per
month?
TR = R * Q
$23,000 = .90 * Q
23,000 = .90Q
.90
.90
Q= 25, 555.5
E. Plot TC and TR. Where do you get your values for TC and TR?
Pick quantities above and below the breakeven point (46, 000
pieces), such as 10,000, 15,000, 20,000, 50,000 and 60,000 and
solve TC and TR for those quantities. Plot both TC and TR with
quantity on the x-axis and $ on the y-axis.
TC = FC + (VC * Q)
TC 10,000 pieces = 9,200 + (.70 * 10,000)
TC 10,000 pieces = $16,200
TR = R * Q
TR10,000pieces = .90 * 10,000
TR10,000pieces = $9,000
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At a production quantity of 10,000 pieces, are we making money?
How much?
TC 20,000 pieces = 9,200 + (.70 *20,000) TR 20,000 pieces = .90 * 20,000
TC 20,000 pieces = $23,200
TR 20,000 pieces = $18,000
TC 60,000 pieces = 9,200 + (.70 *60,000)
TC 60,000 pieces = $51,200
TR 60,000 pieces = .90 * 60,000
TR 60,000 pieces = $54,000
Total Cost and Total Revenue Plot
$
70,000 |
|
60,000 |
|
50,000 |
|
40,000 |
|
30,000 |
|
20,000 |
|
10,000 |
|
0
|________________________________________________________________
5
10
15
20
25
30
35
40
45
50
Quantity (in thousands)
4
Total Cost and Total Revenue
70000
60000
50000
$
40000
30000
20000
10000
0
10,000 30,000 50,000 70,000
Quantity
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Problem 1
1. Determine the utilization and efficiency for each situation:
Utilization =
Actual Output
Design capacity
Efficiency =
Actual Output
Effective capacity
a. a loan processing operation that processes an average of 7
loans/day. The operation has a design capacity of 10 loans per day
and an effective capacity of 8 loans/day.
Utilization = 7 loans/day
10 loans/day
= .70 or 70%
What could cause the utilization to be less than 100%?
Efficiency = 7 loans/day = .875 or 87.5%
8 loans/day
b. a furnace repair team that services an average of four furnaces a
day if the design capacity is six furnaces a day and the effective
capacity is five furnaces per day.
Utilization = 4 furnaces/day = .6666 or 66.67%
6 furnaces/day
Efficiency = 4 furnaces/day = .80 or 80%
6 furnaces/day
c. Would you say that systems that have higher efficiency ratios
than other systems will always have higher utilization ratios than
other systems? Explain.
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Problem 4
A small firm intends to increase the capacity of a bottleneck
operation by adding a new machine. Two alternatives A & B have
been identified and the costs and revenues associated with each
have been estimated. Annual fixed costs for A would be $40,000
and $30,000 for B; Variable costs per unit would be $10 for A and
$11 for B; and revenue per unit would be $15.
Machine A
FC = $40,000
v=$10
R=$15
Machine B
FC=$30,000
v=$11
R=$15
(a) Determine each alternative’s Break-even point in units.
QBEP =
FC
R – VC
Machine A
QBEP =
FC
R – VC
Machine B
QBEP =
FC
R – VC
QBEP =
QBEP =
QBEP =
QBEP =
40,000
15-10
40,000
5
8,000 units
30,000
15 – 11
QBEP =
30,000
4
QBEP = 7,500 units
If demand was 7800 units what should you do?
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(b) at what volume of output would the two alternatives yield the
same profit?
Profit
= Q ( R - v) - FC
Profit A
= Profit B
Q ( R - v) - FC
= Q ( R - v) - FC
Q(15-10) - 40,000 = Q(15-11) - 30,000
Q(5) - 40,000
= Q(4) - 30,000
Q =10,000 units
(c) If your expected annual demand is 12,000 units, which
alternative yields higher profit?
Profit A
Profit A = Q ( R - v) - FC
Profit A = 12, 000 ( 15 -10) - 40,000
Profit A = 12,000 (5) - 40,000
Profit A = $20,000
Profit B
Profit B = Q ( R - v) - FC
Profit B = 12,000 (15 - 11) - 30,000
Profit B = 12,000 (4) - 30,000
Profit B = $18,000
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Problem 5
D= 30,000 pens
FC = $25,000
v = $.37
(a). Find the breakeven quantity if pens sell for $1.
R=$1
QBEP =
FC
R – VC
QBEP =
25,000
1 – .37
QBEP =
25,000
.63
QBEP =
39,682.53 Can you have .53 of a pen? Which
direction should you round?
(b) At what price must pens be sold to obtain a monthly profit of
$15,000 assuming estimated demand materializes? (What variable
are you going to solve for?)
Profit = Q ( R - v) - FC
$15,000 = 30,000 ( R -$.37) - $25,000
$15,000 = 30,000R - 11,100 - 25,000
$15,000 = 30,000R - 36,100
$51,100 = 30,000R
51,100 = 30,000R
30,000
30,000
1.70333=R
How do you handle the decimal places? If you charged $1.70 per pen
would you yield a monthly profit of $15,000? What should the selling
price be?
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